Industrial pumping takes many forms, all with the general requirement of transporting fluids or slurries through a process stream. Pumps are selected based on the application requirements including head pressure, metering accuracy, temperature, particle tolerance, fluid viscosity, cost, safety, service rate and a variety of other parameters. Pumps can generally be classified in two categories. Positive displacement pumps isolate discrete volumes of the working fluid and force them to move in a controlled direction. Kinetic pumps operate by adding kinetic energy to the system which creates a local increase in fluid velocity. Kinetic energy is converted to potential energy, i.e. pressure, at the pump output.
FIGS. 1-3 show a variety of different positive displacement pumps. In FIG. 1, a lobe pump is illustrated. This pump type is designed for low pressure, high volume applications where high particle loading may be an issue. The rotating lobes 2, 2′ of the pump head 1 are intentionally designed with loose tolerances to prevent physical contact and wear. The loose mechanical tolerance allows pressurized fluid to leak back to the low pressure side. This limits the pressure head the pump can reach generally to less than 20 bar. FIG. 2 illustrates a second type of rotary pump called an external gear pump. The pumping operation is similar to the lobe pump, but tolerances of the gear pump may be made arbitrarily close. As a result, gear pumps can obtain pressures heads of several hundred bar and pump fluids of viscosities from 0.05 to 100000 cP. Significant wear of the gears 3, 3′, especially at high pressure and temperature results in variable leakage back to the low pressure side. Both styles of rotary pumps can be isolated in sealed enclosures 4 and driven by magnetically coupled pump motors. This has the tremendous advantage of preventing external leaks of fluid without the use of dynamic seals. Magnetic coupling has lower torque limits than direct drive, however, so gear pumps are generally available only to less than 30 to 50 bar differential pressure. A final valuable characteristic to lobe and gear pumps is that they are considered both continuous and pulseless.
Reciprocating pumps, such as the one shown in FIG. 3, remain a primary industrial means of pumping fluids when high purity, high pressure [e.g. >100 bar to more than 1000 bar] and high precision [e.g. <1% flow variation] are needed. Reciprocating pumps come in several formats including mechanical and pneumatic piston pumps, and mechanical and hydraulic diaphragm pumps. Such pumps are characterized by having one or more heads 5 which transfer fluid between a low pressure input and a higher pressure output. Each pump head contains a means of physically adjusting the internal volume available to the pumped fluid. In operation, each pump head 5 uses a piston 8 driven by cam 9 that alternately aspirates fluid from the input 6 by increasing the available pump head volume, then dispenses the fluid to the output 7 by decreasing this volume. Most reciprocating pumps are designed to flow in only one direction. Flow direction is controlled by a series of check valves 6′, 7′ that isolate the pump head from the output pressure during aspiration and from the input pressure during dispensing. The output pressure is generally controlled, not by the pump, but rather by the downstream resistance-to-flow of the process flow stream serviced by the pump.
Reciprocating pumps are characterized by the number of pump heads they utilize. A pump with a single pump head is referred to as a simplex pump. Duplex, Triplex and Quad pumps refer to pumps with two, three and four heads respectively. Two or more pumps heads are required to provide pseudo-continuous flow since one pump head can be delivering while the other is aspirating. However, since the very nature of the movement involves stopping and restarting in opposing motions, reciprocating pumps can only emulate continuous rotary pumps approximately. In general, the greater number of pump heads for a given flow rate, the lower the pulsation of the output stream.
When fluid being pumped by a piston pump is relatively incompressible, these pumps are frequently referred to as metering pumps, since the volumetric flow of the fluid is presumed to match the mechanical volumetric displacement of the piston or diaphragm in the pump head. An excellent example of a metering application of a reciprocating pump is a low pressure syringe pump, in which a glass syringe draws in an aqueous solution and dispenses it very accurately to a downstream reservoir. Under this low pressure use [generally less than 2 bar] the volumetric compression of aqueous solutions is almost immeasurable and thus the presumption of accurate displacement is correct.
When reciprocating pumps are used with very compressible fluids such as permanent gasses, they are frequently called compressors or gas boosters. Gas boosters represent an ideal example of the influence of fluid compressibility on pump performance. In this case, the typical application is to increase the pressure of the gas between the input and output. A fundamental characteristic of gas boosters is the compression ratio. The compression ratio is simply the ratio of the maximum fluid volume a pump head can isolate between its check valves at the peak of its intake stroke to the minimum volume it can reduce to at the end of its delivery stroke. Hence, a compression ration of 7:1 indicates the total volume at intake is seven times greater than the residual fluid volume at the end of delivery.
FIG. 4 displays the compression or delivery stroke of a pump head in a gas booster. In this figure, the pump head 10 is comprised of cylinder 12, piston 14, and input and output check valves 16 and 18 respectively. During the delivery stroke, the cylinder internal volume has three distinct regions: compression volume 20, delivery volume 22 and residual volume 24. During compression, volume is systematically decreased and thermodynamic work is performed on the fluid and it tends to heat up. Higher temperature and lower volume cause an increase in the fluid pressure. The effect of the temperature increase is that the fluid reaches the delivery pressure earlier in the pump stroke than calculated by a simple isothermal volumetric displacement. If no heat were lost to the piston or cylinder walls the heating would be called adiabatic heating, which can be readily calculated from entropy tables for a given gas. Heat generated in the fluid is generally a source of inefficiency since it delivers the gas at a considerably lower density than desired. A cooling step is frequently required in the boosting process to remove the waste heat of compression so that downstream vessels can be filled more densely with the pressurized gas.
It is nearly impossible for a robust pump head design to leave no residual fluid at the end of the delivery stroke. Too close machining tolerances can cause a greater rate of wear and early failure of sealing surfaces. FIG. 4 shows the residual volume of gas remaining at the end of the piston stroke. In general, for gas pressure boosting applications it is very desirable to make this volume as small as possible and to make the compression ratio large. Hot residual gas in the pump head causes a further decrease in pumping efficiency, since it must first expand to below the input pressure before new fluid can enter the pump head during aspiration. Finally, compressive heating of the pump head itself will warm the entering gas to a lower density and reduce the amount of fluid entering with each aspiration.
An examination of the output flow of a gas booster reveals the ultimate difficulty in pumping compressible fluids. For each pump head, the aspirate stroke is expected only to fill the pump head volume and not deliver fluid to the output. The dispense stroke, on the other hand, is expected to deliver fluid to the output. In a piston based gas booster, as the piston moves forward to expel the fluid, temperature and pressure rise, but no fluid is released until the output pressure is reached. If the input pressure is 1 bar and the output pressure is 2 bar, almost half the piston stroke is used just to compress the fluid before delivery begins. As output pressure rises, a smaller and smaller volume of the delivery stroke is released to the output stream. By the time an output pressure of 7 bar is achieved in a booster with a 7:1 compression ratio almost the entire stroke is used for compression with little or no volume released to the output stream.
If aspiration and dispense strokes are of equal duration, fluid is delivered only 25% of the complete pump cycle in the 2 bar case. Even in a duplex booster pump, flow would only occur 50% of the time. By the time 7 bar output pressure was achieved, the pump would be delivering <1% of the time. As a result, most booster pump applications are pressure based and not flow based. These are not considered metering pumps at all since the work for compression makes it impossible to reliably calculate the volume of delivery per stroke.
Some applications require pumps that can meter fluids continuously and accurately at high pressure. For all fluids, including gasses, liquefied gasses, liquids and supercritical fluids, pressurization results in corresponding decrease in volume and increase in temperature to some degree. In general the compression effect is orders of magnitude different between permanent gasses such as Helium, liquefied gasses such as liquid carbon dioxide [LCO2] and true liquids such as water. At high enough output pressures, however, even water must be measurably compressed before being delivered to an output flow of a pump flow stream.
Water essentially behaves like a spring with a definable force constant that indicates how much volume change will occur per applied unit of pressure. This force constant is referred to as compressibility and is often reported in units of inverse bar [bar−1]. The generally accepted compressibility value for water at 20 C is 46×10−6 bar−1. Hence at 1 bar additional pressure, a volume of water would reduce 0.0046%; at 10 bar 0.046%; at 100 bar 0.46% and at 1000 bar 4.6%. In fact, water does not behave as a perfect spring and the compressibility value tends to become smaller at very high pressure so the 4.6% volume change is somewhat overstated, nevertheless it is clear that between 100 and 1000 bar a measurable portion of the dispensing pump stroke will be dedicated to compression of the water and thus cause an interruption to the continuous flow of a standard duplex pump. Water is considered one of the more incompressible liquids. Table 1 lists compressibility values for other representative organic solvents at 20° C. Generally these organic solvents range from two to three times more compressible than water.
TABLE 1Compressibility valuesfor various pure liquids at 20 C.CompressibilityLiquid(×10{circumflex over ( )}6 bar −1)Water46Tetrahydrofuran93Acetonitrile99Benzene94-95Chloroform 97-101Methylene97chlorideCarbon103-105tetrachlorideEthanol110-112Methanol121-123Acetone123-127n-Heptane140-145n-Hexane150-165Diethyl ether184-187
In practical terms then, for a reciprocating pump, compressibility is the fraction of the piston stroke required to increase the fluid pressure to delivery pressure. Compressibility compensation refers to reducing the period of deficit flow and/or adding extra flow to the flow path to compensate for this deficit. Also for the purpose of clarity, a compressible fluid shall be defined in terms of the fluids density variation in going through the metering pump and the corresponding need for compensation. It is common for high pressure metering pumps to have specified volumetric flow accuracy relative to the operational or maximum flow value. Without further calibration, pumps must rely on the assumption that mechanical displacement is equivalent to fluidic delivery. Hence a pump specified to 1% accuracy could not compress the aspirated fluid by more than 1% during the piston delivery stroke. Compressible fluids would be those that exceed this amount of compression [and corresponding change in density] during a delivery stroke. As a result, compressibility compensation is required to bring the pump to the operating specification.
Whether a fluid is compressible by this definition is tied to the delivery pressure of the fluid. A single fluid aspirated from an atmospheric reservoir, may be below this compressible fluid threshold at low delivery pressures but above it at high delivery pressures. For example, for a pump with a 1% accuracy specification, water [compressibility=46×10−6 bar−1] does not become compressible until it reaches approximately 225 bar, while hexane [compressibility=150×10−6 bar−1] becomes compressible at approximately 65 bar. When a fluid's compressibility exceeds the pump specification at some operational level, some action must be taken to adjust the pump's performance. This corrective action is generally referred to as compressibility compensation.
Values of the compressibility for a given liquid are dependent on both temperature and pressure. Generally as pressure increases the compressibility value goes down while at higher temperatures the value increases. Other factors such as dissolved gasses in the liquid can affect the compressibility value. Mixing two or more liquids can have unpredictable effects on the solutions compressibility. Table 2 shows the very nonlinear behavior of mixtures of water and methanol at 20 C.
TABLE 2Compressibility Valuesfor Water:Methanol MixturesWater-methanol,Compressibility(v-v)(×10{circumflex over ( )}6 bar −1)100-0 4680-204060-404650-505240-605620-808610-90117 0-100121
Many laboratory and industrial applications require continuous high pressure flow of fluids similar to those listed in Tables 1 and 2. One example is high pressure mixing of fluids, where periodic lapses of flow from one process stream will cause significant local concentration variability. Such variability can lead to improper dosage levels of active pharmaceutical ingredients or imbalance in the ratio of reactants in chemical flow reactors. At the laboratory scale, a prime example of the need for continuous high pressure flow is the case of high pressure metering pumps used in high performance liquid chromatography [HPLC]. Modern HPLC systems are commonly comprised of two separate pump modules to allow the high pressure, controlled mixing of two solvents at a time to create a well mixed mobile phase for chromatographic elution.
FIG. 5 shows the basic components for an HPLC pump of prior art. HPLC pump 30 is an example of an electric cam driven pump. In this case motor 32 rotates shaft 34 to rotate eccentric cams 36 and 38 to provide a reciprocating motion of pistons 40 and 42 contained in pump heads 44 and 46 respectively. As each piston aspirates, fluid is drawn from fluid reservoir 56 through input check valve 48 or 50 respectively. Output check valve 52 or 54 remains sealed during aspiration. During the delivery stroke, input check valve 48 or 50 is shut while output check valve 52 or 54 opens to deliver fluid to process stream 58. The cam drive shown in FIG. 5 is just one example of an HPLC pump. Others would include ball screw drives, pneumatic drives and hydraulic drives coupled to the pistons 40 and 44. Much of the remaining discussion focuses on pumping a fluid using compression compensation of laboratory-type HPLC type pumps that are similar in design to pump 30.
Requirements for pumps used in typical laboratory HPLC instruments are very demanding. Pumps must be able to deliver at very high pressures [up to 400 bar for traditional HPLC and as high as 1000 bar for recent ultrahigh performance LC systems]. A 2000 bar ultrahigh performance LC system is expected. HPLC pumps must also be able to handle fluids of ultra-high purity without contributing detectable contamination. In addition, for a given flow rate, the volumetric delivery of fluid is expected to remain constant within narrow limits [<1% variation] across the majority of the operational pressure range. Finally, the same pump is also expected to vary flow precisely over at least an order of magnitude of range in periods as short as one minute. This is the result of the need for a technique called gradient elution in which the two solvents controlled by separate pumps are systematically adjusted in relative composition from a weakly to a strongly eluting mixture while maintaining a constant combined flow rate.
An interesting effect of the mixing of two different solvents is that the viscosity of the combined mixture may vary widely over the course of the gradient run. As viscosity increases the resistance to flow of the chromatographic system causes a pressure rise. Thus even as one solvent is decreasing in its flow rate during the gradient elution, the pressure the pump experiences can be rising. FIG. 6 displays the viscosity behavior of various compositions of two binary mixtures: water:methanol 62 and CO2:methanol 64. Mole fraction of methanol is graphed on the x-axis and viscosity in millipascal-seconds is graphed on the y-axis 68. For typical HPLC applications, the water: methanol plot 62 clearly demonstrates extreme nonlinearity that can occur over the range of compositions. Each pump must be able to adjust to both varying output pressure and flow during gradient runs. Further, most long term applications require that the pumps must repeat this performance within a specification limit over their useful lifetime in order to provide truly valid data for the HPLC system.
In order to meet such demanding performance specifications, Modern HPLC pumps must address the issue of compressibility. Compounding the problem of compressibility is the fact that a majority of standard HPLC pumps have compression ratios less than 3:1. This means that there exists a minimum residual volume of 50% of the full stroke volume of each piston that never leaves the pump head's internal volume. This residual volume must be compressed and expanded on each stroke which adds a burden of at least 50% to the compressibility compensation effort. This sets a significantly lower limit for a given fluid on the maximum pressure at which it may be effectively pumped.
To counter the periodic flow lapses resulting from fluid compressibility, pump manufacturers have devised a number of techniques to suppress their negative effects. Pulse dampeners are routinely used in high pressure equipment to attenuate the pressure fluctuations associated with periodic discontinuities in flow. Pulse dampening attenuates pressure noise from the system, but does not always correct flow issues. Consider the case of pumping a moderately compressible liquid at high pressure. The piston is set to deliver at a fixed rate of displacement to achieve the desired flow. Since the compression part of the stroke delivers no flow without makeup or compensating flow, followed by the delivery portion which delivers at the correct flow rate, only negative flow pressure pulsations are seen at the pump output. No amount of pulse dampening will smooth the flow to the desired flow rate. It will always be less than required. A common technique to counter this issue is simply to increase the mechanical rate of the piston so that the average flow matches the expected flow. However, as seen earlier, the amount of compression needed per stroke varies with output pressure. As a result, very specific knowledge of the fluid characteristics would be needed to make this correction at all flows and pressures.
Simple correction to improve average flow also neglects yet another problem, local variations in the flow compositions. It is a frequent practice to place a single pulse dampener in binary pumps [a single pump module which contains two separate duplex pumps] at a location downstream of the mixing point of the two fluids. Thus each flow lapse of one pump due to compression results in a segment of flow that is dramatically enriched in the other fluid. This local enrichment, especially of high strength elution solvents can cause serious perturbations of the separation in HPLC. Further, since composition changes usually are accompanied by detectable changes in the refractive index of the fluid, significant noise can be experienced at any optical detectors in the flow system. This noise typically limits the ability of the system to detect very small quantities of material in the flow stream.
To limit the effect of compression, HPLC pump manufacturers have also attempted to shorten or eliminate the compression time. This has been done by accelerating the piston displacement during compression to minimize the period of flow lapse. Again, while a fixed acceleration period is useful over a limited range of pressures, in order to compensate over the entire pump range the acceleration period must be proportional to the output pressure. This feature has been accomplished in some modern HPLC pumps which can allow entry of CCF values up to 150×1−6 bar−1.
In the last several years, much focus has been placed on new ultrahigh performance chromatographic systems extending beyond the 400 bar pressure limit. This change has dramatically increased the awareness of compressibility as a major factor in pump performance. Traditional pumps have been redesigned to improve compression ratios. Special calibration algorithms have been adapted to determine empirically the compressibility of fluids over the entire range of pump operation to account for the actual nonlinearity of compression correction factors.
One area that has not been well addressed in the pursuit of higher pressures is the thermodynamic work that must be performed on the pumped fluids. As ultimate pressures reach 1000 or even 2000 bar, even well behaved fluids such as listed in Table 1 experience significant compression. Just as in the gas booster example above, significant compression, especially at the accelerated rate required for compression compensation, can result in significant heating of the fluid. Heating in turn leads to variability in fluid density and compressibility. Further, heat generated in the fluid during compression can communicate to pump head walls and warm incoming fluid further affecting density. Over the course of variable gradient flow, such factors are continuously varying and make it quite difficult to determine precise composition of the mixed components of the binary mobile phase.
Compressibility levels encountered in ultrahigh performance chromatographic systems are very similar to those encountered in supercritical fluid chromatography (SFC) over the last twenty years. SFC is a subset of traditional HPLC that uses liquefied CO2 as one of the components of the mobile phase. As a liquefied gas, CO2 must be delivered at high pressure to the pump head in order to remain in the liquid state. This is normally accomplished by connecting a tank containing both liquid and vapor CO2 in thermal equilibrium. A dip tube in communication with the CO2 liquid of the tank is plumbed directly to the pump head. Generally, chilling of the pump head and pre-chilling of the fluid are necessary to insure that CO2 remains in the liquid state during pump aspiration. Special grades of high purity CO2 are used in SFC to prevent dissolved components of less pure CO2 from affecting the optical clarity of the mobile phase. Mixtures of CO2 and common organic solvents also tend to have higher changes in refractive index than corresponding water: organic solvent mixtures so that small rapid variations in composition are more observable with optical detectors.
As mentioned, pumping of liquid CO2 takes special precautions to insure a continuous liquid supply into the pump head. The compressibility of liquid CO2 is also a major factor since it is typically as much as ten fold higher than most of the organic liquids mentioned in Table 1. Further, compression of CO2 between 60 bar [approximate tank pressure] and 400 bar [the maximum system pressure] can raise the fluid temperature more than 25 C. Such a temperature rise dramatically alters the density of the delivered fluid and introduces even more requirements for pump control.
The vast majority of commercial SFC pumps are modified HPLC pump designs. One manufacture uses the equation of state of CO2 to calculate fluid compressibility at various pumping pressures. A second manufacturer uses mass flow sensors to determine the average mass flow of the system and adjusts the pump speed to maintain a controlled average mass flow. Another reported technique is to use a specialized duplex pump where each piston is controlled by an independent motor. Pressure sensors allow the filling pump head to pre-compress the fluid to 90% of the output pressure as part of the filling sequence. Triplex pumps are reported that allegedly further reduce flow pulsation. Special algorithms have been created to surge pumps slightly beyond full compression to add a small excess of CO2 flow immediately adjacent to the CO2 deficient region and then allowed the segments to mix by longitudinal diffusion. For all the efforts to date, SFC analysis is still considered to be of lower sensitivity and poorer quantitation limits than standard HPLC. A significant reason for this is higher baseline noise directly related to the methods employed to fully compensate for compressibility.
In most reciprocating pumps an extra flow is added at the end of the compression stroke to compensate for the lack of flow during compression. Without this compensating flow, the pump will deliver inaccurate flow and compositions which become unintended functions of the delivery pressure. Thus, there is a period of no flow, followed by a period of excess flow. The two are intended to cancel each other out. While such compensation assures accurate flow and composition, it increases short term flow and pressure noise, which increases detector noise and degrades detection limits. The much higher compressibility of CO2 compared to normal liquids used in HPLC results in a much longer lapse and larger compensating flow, accounts for most of the degradation in detector noise previously observed in SFC.
Despite the poorer limits of detection, SFC enjoys high popularity in the areas of both preparative separation and analysis. SFC is the technique of choice in the rapidly growing area of chiral separation. This technique is also shown to be two to five times faster than traditional HPLC in separating both chiral and achiral mixtures. In fact, SFC competes favorably with the most advanced state-of-the-art implementations of ultrahigh performance chromatographic systems without the need for extreme pressures, special separation columns and vendor specific consumable hardware. As a result, a high interest remains for this technique if it can be brought closer to the low levels of quantitation available to HPLC.
The general steps of pumping with a piston pump involve aspiration of working fluid into the pump chamber, compressing the fluid to the pump output pressure and delivering the compressed fluid to the output flow stream. In the course of this process thermodynamic work is performed on the working fluid which results in temperature and density changes of the fluid. In addition, the amount of work and corresponding physical change done to the fluid is dependent on both total pressure rise required within the pump head and the physical characteristics of the fluid itself. This variability leads to the poorly metered pumping of fluids of unknown density and requires use of correction factors that are generally inadequate to provide pulse free flow from the pump head. As a result, both systematic and local variations in composition can easily arise in the mixed flow stream of binary and ternary pump systems.
While this discussion has focused a great deal on the needs of low-noise, precise, continuous high pressure pumping in chromatography, the need is truly general. Thus, there is a need for a solution for metering a compressible fluid without the variations that degrade overall quality of the process stream and frequently require addition of further components to correct this quality at the expense of speed, cost or energy efficiency in the process stream.